1. Field of the Invention
The present invention generally relates to a vibration control system and, more particularly, to an interconnected distributed network of actuator devices for the control of damping vibrations in two dimensional mechanical structures.
2. Description of the Prior Art
Many industries such as the automobile industry, the aerospace industry and even the oil exploration industry expend great resources and energy to develop mechanisms for controlling vibrations in mechanical structures (e.g., automobiles, airplanes, pipelines, etc.). These vibrations are not only troublesome from a marketing and consumer satisfaction standpoint, but may equally be troublesome from a safety and environmental standpoint. That is, excess vibrations may actually cause damage to the mechanical structure leading to cracks and excessive noise, and in some extreme cases, a catastrophic failure of the mechanical structure, itself. In this latter situation, the failure of the mechanical structure may result in large expenditures in replacement costs, manufacturing costs as well as manpower and equipment. By way of one example, improper or inadequate vibration control in an oil pipeline may result in a failure of that pipeline. This, in turn, may result in an oil spill which can have a devastating environmental impact. To clean this oil spill, millions of dollars may have to be spent for rehabilitating the environment as well as replacing the pipeline, itself.
It is for the above reasons, and many others, that vibration control (e.g., damping of vibrations) is a very important aspect of engineering work when designing a mechanical structure. To minimize vibrations, engineers have devised many systems including active and passive control systems. One such active control system is piezoelectric (PZT) actuator technology. In this technology, actuators are used to dampen and control mechanical structure vibrations. It has been found, however, that these types of systems are limited in nature, and do not always provide adequate damping of the vibrations in a mechanical structure.
Two common limiting features of control systems presently used for vibration damping include:
the differentiation between the sensing and the actuation systems, and
the localization of PZT actuators at a small number of specific sites on the vibrating structure.
Both of these above features are limits to control efficiency. Indeed, the first factor implies the need for high power in concentrated structural regions and the need for a coordinating active system that controls the actuator action in response to the input from the sensors. On the other hand, the latter factor implies an optimal localization problem (for both actuators and sensors), the solutions of which depend on the particular mechanical vibration mode under consideration. Moreover, it is difficult to optimize the characteristics of these commonly used control systems to obtain low equivalent impedances (these are required to allow a relevant energy transformation from the mechanical to the electrical form) and efficiently drive the PZT actuators.
Some efforts have been made to overcome the first of these drawbacks. In particular, the concept of self-sensing actuators has been introduced in recent years. In this case, an ad hoc electric circuit is connected to the PZT actuator allowing for a two-fold behavior (as a sensor and as a control device). However, every actuator remains isolated and its electro-mechanical action has to be coordinated with the rest of the structure. Also, although a great number of actuators have been considered to control the shape of plates and shells, these systems still do not control the damping of vibrations.
The articles xe2x80x9cContinuum Modelling of Piezoelectro-mechanical Truss Beams: an application to vibration Dampingxe2x80x9d, by Francesco Dell""Isola et al., Archive of Applied Mechanics 68 (1998), pp. 1-19, Springer. Verlag, and xe2x80x9cBendingxe2x80x94Waves Damping in Truss Beams by Electrical Transmission Line with PZT Actuatorsxe2x80x9d Francesco Dell""Isola et al., Archive of Applied Mechanics 68 (1998), pp. 626-636, Springer Verlag discuss several differential equations which may be used to control vibrations in a one dimensional mechanical structure. In these articles only a one-dimensional case is treated with no discussion of a two-dimensional case (which is not a trivial extension). Also, these articles do not provide any specific arrangement of devices, but merely suggest an application concerning a given type of truss beam equipped with extensional actuators. Both xe2x80x9cContinuum Modelling of Piezoelectro-mechanical Truss Beams: an application to vibration Dampingxe2x80x9d and xe2x80x9cBendingxe2x80x94Waves Damping in Truss Beams by Electrical Transmission Line with PZT Actuatorsxe2x80x9d are incorporated by reference herein in their entirety.
By way of example, FIG. 1 shows a connection arrangement of actuators for controlling extensional and torsional vibration of a one-dimensional structure (e.g., beam structure) as described in the above papers. The actuators shown in FIG. 1 are preferably PZT actuators which are formed in an electric network. In FIG. 1, a set of three PZT actuators 10a, 10b and 10c are each connected in parallel to respective impedances 12a, 12b and 12c. A transmission line with a plurality of serially connected impedances 14a, 14b, 14c connects the parallel arrangement of actuators, and capacitors. The connection arrangement shown in FIG. 1 can be expanded to include more than three parallel arrangements of actuators and impedances positioned between the serially connected impedances.
FIG. 2 shows an arrangement of interconnected piezoelectric PZT actuators disposed on a beam or one dimensional structure according to FIG. 1. In this assembled system, the PZT actuators 10a-10e are PZT patches arranged along the neutral axis of the beam 16. As noted in the above papers, the governing equations for the electric network of FIGS. 1 and 2 has the same form as the equations governing the behavior of the extensional and torsional waves in the beam-like structure (e.g., one-dimensional structure).
It is therefore an object of the present invention to provide a system for controlling the damping of vibrations in a two dimensional mechanical structure.
It is another object of the present invention to provide a system which exploits an interconnection among actuators to form a continuous electric network.
It is yet another object of the present invention to provide a system which heightens a synergic response of an interconnected set of actuators to mechanical vibrations in a two-dimensional vibrating structure.
It is still yet another object of the present invention to provide a system which exploits an internal resonance phenomenon between structural modes and electric modes to optimize control efficiency.
It is also another object of the present invention to provide a system which requires lower performances of PZT actuators.
It is an additional object of the present invention to provide a system which efficiently transforms mechanical energy into electrical energy.
It is yet an additional object of the present invention to provide a system which uses the resonance of the two-dimensional vibrating mechanical structure to transform energy between the structure to be controlled and the controlling network.
It is also an additional object of the present invention to provide a system which bypasses the problems of the optimum position of actuators and sensors.
According to the invention, a system is provided for controlling the damping of vibrations in a two dimensional mechanical structure. The system includes at least two actuating devices and a transmission line connecting the at least two actuating devices. The transmission line and the at least two actuating devices form a continuous distributed network which exploits a resonance of a two-dimensional vibrating structure to transform mechanical energy into electrical energy and transfer the electrical energy along the transmission line and between the at least two actuating devices. The actuating devices may include a parallel arrangement of piezoelectric (PZT) actuators and impedances.
In another aspect of the present invention a system for damping a vibrating body is provided. The system includes at least two actuators and at least two impedances arranged in parallel. A transmission line connects the parallel arrangement of the actuators and the impedances to form a continuous distributed network. The governing equations for the continuous distributed network of the parallel arrangement of the actuators and the impedances has substantially a similar form as equations governing a behavior of extensional and torsional waves in the two-dimensional vibrating structure.